Finite Group Databasebeta

← #11796747

Subgroups — #11796747

Order 1152.

406 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3718C211yesmaximal, characteristic
2C2×#63773C211yesmaximal, characteristic
3#10591138C211yesmaximal, characteristic
4#10590062C214yesmaximal, complemented
5C22×C3×Dic6—21no—
6C22×C3⋊(C3⋊C8)C2211yescharacteristic
7C3×#926—21no—
8C2×#3718—21no—
9C2×#3718—22no—
10C2×#3718C414yescomplemented
11C2×#3718C2212yes—
12#63773—22no—
13C2×#3708C2212yes—
14#63576C2212yes—
15#63574—21no—
16C22×#216—61no—
17#4998—61no—
18C22×C32×C4D411yescharacteristic
19C22×C3×Dic3—41no—
20C2×C3×Dic6—24no—
21C2×C3×Dic6—22no—
22C2×C3×Dic6—41no—
23C2×C3×Dic6—42no—
24C2×C3⋊(C3⋊C8)C2×C412yes—
25C2×C3⋊(C3⋊C8)D411yescharacteristic
26C2×C3⋊(C3⋊C8)D412yes—
27C2×C3⋊(C3⋊C8)C2311yescharacteristic
28C3×#217—41no—
29C3×C4⋊Dic3—22no—
30C3×C4×Dic3—41no—
31#3718—24no—
32#3718—22no—
33#3718C2×C414yes—
34#3708—22no—
35#2141—91nomaximal, Sylow
36C22×C3×Q8—61no—
37C22×Dic6—21no—
38C3×#117—61no—
39C2×#216—64no—
40C2×#216—62no—
41C2×#216—62no—
42C2×#216—64no—
43#926—21no—
44C22×C3⋊C8—61no—
45C22×C3⋊C8—61no—
46#808—62no—
47#807—62no—
48C23×C32D811yescharacteristic
49C2×C32×C4C22⋊C412yes—
50C2×C32×C4D811yescharacteristic
51C2×C32×C4SD1612yes—
52C2×C32×C4C2×D411yescharacteristic
53C2×C3×Dic3—44no—
54C2×C3×Dic3—42no—
55C2×C3×Dic3—42no—
56C3×Dic6—24no—
57C3×Dic6—44no—
58C3×Dic6—42no—
59C3⋊(C3⋊C8)C22⋊C412yes—
60C3⋊(C3⋊C8)C22×C411yescharacteristic
61C3⋊(C3⋊C8)C2×D411yescharacteristic
62C22×Q16—91no—
63C2×M32—91no—
64#427—91no—
65#358—94no—
66C2×C3×Q8—62no—
67C2×C3×Q8—64no—
68C2×C3×Q8—121no—
69C2×C3×Q8—122no—
70C22×C3×C4—21no—
71C22×C3×C4—21no—
72C22×C3×C4—121no—
73C22×Dic3—41no—
74C2×Dic6—22no—
75C2×Dic6—24no—
76C2×Dic6—41no—
77C2×Dic6—42no—
78C3×C4⋊C4—62no—
79C3×C22⋊C4—121no—
80C3×C42—121no—
81#217—41no—
82#216—64no—
83#216—68no—
84#216—64no—
85C4⋊Dic3—22no—
86C4×Dic3—41no—
87C2×C3⋊C8—61no—
88C2×C3⋊C8—61no—
89C2×C3⋊C8—62no—
90C2×C3⋊C8—62no—
91C2×C3⋊C8—62no—
92C2×C3⋊C8—61no—
93C2×C3⋊C8—62no—
94C2×C3⋊C8—61no—
95C22×C32—22no—
96C22×C32#10212yes—
97C22×C32C2×D811yescharacteristic
98C32×C4#10212yes—
99C32×C4C2×C22⋊C411yescharacteristic
100C32×C4C2×SD1611yescharacteristic
101C3×Dic3—44no—
102C3×Dic3—82no—
103C22×Q8—61no—
104C2×Q16—92no—
105C2×Q16—94no—
106C2×Q16—181no—
107C2×Q16—182no—
108C22×C8—91no—
109#117—61no—
110M32—182no—
111C2×C16—92no—
112#107—92no—
113#106—181no—
114C23×C3—21no—
115C23×C3—21no—
116C3×Q8—64no—
117C3×Q8—122no—
118C3×Q8—124no—
119C2×C3×C4—21no—
120C2×C3×C4—21no—
121C2×C3×C4—22no—
122C2×C3×C4—22no—
123C2×C3×C4—21no—
124C2×C3×C4—21no—
125C2×C3×C4—22no—
126C2×C3×C4—22no—
127C2×C3×C4—122no—
128C2×C3×C4—124no—
129C2×C3×C4—122no—
130C2×Dic3—42no—
131C2×Dic3—44no—
132C2×Dic3—42no—
133Dic6—24no—
134Dic6—42no—
135Dic6—44no—
136C3⋊C8—62no—
137C3⋊C8—62no—
138C3⋊C8—61no—
139C3⋊C8—61no—
140C3⋊C8—61no—
141C3⋊C8—61no—
142C2×C32—22no—
143C2×C32C2×#10211yescharacteristic
144C2×C32#51012yes—
145C2×Q8—62no—
146C2×Q8—64no—
147C2×Q8—121no—
148C2×Q8—122no—
149C22×C4—121no—
150C22×C4GO+(4,𝔽2)11yescharacteristic
151Q16—94no—
152Q16—182no—
153Q16—184no—
154C2×C8—91no—
155C2×C8—91no—
156C2×C8—92no—
157C2×C8—92no—
158C4⋊C4—62no—
159C22⋊C4—121no—
160C42—121no—
161C16—182no—
162C22×C3—24no—
163C22×C3—21no—
164C22×C3—21no—
165C22×C3—22no—
166C22×C3—22no—
167C22×C3—42no—
168C3×C4—21no—
169C3×C4—21no—
170C3×C4—21no—
171C3×C4—21no—
172C3×C4—22no—
173C3×C4—22no—
174C3×C4—124no—
175C3×C4—242no—
176Dic3—44no—
177Dic3—82no—
178C32#214111yescharacteristic, complemented, Sylow
179C23#377411yescharacteristic
180Q8—64no—
181Q8—122no—
182Q8—124no—
183C2×C4—122no—
184C2×C4—124no—
185C2×C4—122no—
186C2×C4D32⋊C412yes—
187C2×C4#377411yescharacteristic
188C2×C4#377512yes—
189C2×C4C2×GO+(4,𝔽2)11yescharacteristic
190C8—91no—
191C8—91no—
192C8—92no—
193C2×C3—24no—
194C2×C3—22no—
195C2×C3—22no—
196C2×C3—21no—
197C2×C3—21no—
198C2×C3—42no—
199C22—22no—
200C22#6373912yes—
201C22C2×#377411yescharacteristic
202C4—124no—
203C4—242no—
204C4#6373912yes—
205C4C2×D32⋊C411yescharacteristic
206C4C2×#377511yescharacteristic
207C3—21no—
208C3—21no—
209C2—22no—
210C2#1059333612yes—
211C2C2×#6373911yescharacteristic
subgroupG/H
centerC22C2×#3774
commutatorC3⋊(C3⋊C8)C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×D8
prime radicalC23×C32D8
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#2141
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #10590062C2semidirect
10. C2×#3718C4semidirect
178. C32#2141semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#37182
C2×#637732
#105911382
#105900622
#21419